3 The matrix \(\mathbf { A }\) is \(\left( \begin{array} { r r r } - 1 & 2 & 4
0 & - 1 & - 25
- 3 & 5 & - 1 \end{array} \right)\). Use the Cayley-Hamilton theorem to find \(\mathbf { A } ^ { - 1 }\).
\(4 T\) is the set \(\{ 1,2,3,4 \}\). A binary operation • is defined on \(T\) such that \(a \cdot a = 2\) for all \(a \in T\). It is given that ( \(T , \cdot\) ) is a group.

1. Deduce the identity element in \(T\), giving a reason for your answer.
2. Find the value of \(1 \cdot 3\), showing how the result is obtained.
3. 1. Complete a group table for ( \(T , \bullet\) ).
   2. State with a reason whether the group is abelian.